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A diagram of all knowledge topics.

Topics (also Tech or Innovations) are part of knowledge.

There are around 300 innovations that can be discovered. Many of them have requirements, and many do not, so it's kind of a tech forest/grassland rather than a tree. Notably missing are innovations related to practical labors in the game (which will be added later in development). Only the discovery of literary form topics has any effect on gameplay, as it allows scholars to write new types of books.

Several innovations require innovations from other branches, and since all knowledge is individually tracked, that implies some investigators will need to be at least well-read if not skilled in various topics (there aren't currently joint research projects). There are some old and new mechanisms in place to ensure this happens.

There are 9 "branches" of the knowledge system. Each branch is further divided into categories of topics, such as methodologies, theories, etc.

Discovering Topics

According to a Future of the Fortress reply:

Fortress scholars do activity cycles, the length of which is 1-2 days (whether they are pondering or discussing etc.) Once they get through 50 cycles, it rolls 0-50 vs. the number of completed cycles minus 50 to see if they get "breakthrough credit." So at 51, they have a 2% chance, and at 100, they have a 100% chance. Then, it resets the cycle number to zero and gives them breakthrough credit, based on a skill roll plus 100 (for discuss, the other researchers contribute half of their summed skill rolls.) Based on the difficulty (1-4) of the topic, total lifetime breakthrough credit is then assigned a number of 50-sided dice. An easy topic is dice=credit/2500, then /5000, then /10000, then /20000 for level 4 topics. The number of dice cannot exceed 10. Then roll these dice -- if you get a 50 on any of them, discovery! This is a bit archaic, and I'm not suggesting it works particularly well. But that is how it works. Also: if they fail to get the breakthrough after the 50-sided rolls, they have a 2% chance of switching topics, or if their credit exceeds 100000, they always switch topics (though they keep the credit, so returning to the topic later gives them a decent chance at breakthrough.)

For unskilled roles, some initial back-of-the-envelope calculations and some rough estimates observed through dfHack gives a basic idea of just how long research can take. Note that player testing had found that the skill roll contributes a lot to the breakthrough credit. Even dabbling dwarves can gain over 2000 breakthrough credit at once and may average around 1000 breakthrough credit. Additionally the formula for the skill roll seems to have a very large spread, players have reported as low as 3000 breakthrough credit and as high as 25000 breakthrough credit awarded to a dwarf with legendary skill. Analytically calculating from the algorithm Toady gave, it takes an average of 58.54 cycles to get a breakthrough credit. Player testing has confirmed breakthrough credits typically take 55-65 cycles, so this calculation seems plausible. Likewise, player testing has not shown any correlation between skill level and number of cycles to get breakthrough credit. An unskilled dwarf might average around 120+ cycles to get their first breakthrough die for a level 1 topic. With only a single research die, it would take an average of 2528 cycles to get a breakthrough. Pondering takes slightly over 2 days per cycle, so this would be around 14 years. In a real fortress, the research dice and skill level will be increasing during the process. However, in a real fortress, the scholars will also need to take breaks to eat, drink, and meet other needs. A more reasonable estimate is around 5-10 years for a breakthrough starting with no skills. In short, research takes an unreasonably long time with an unskilled dwarf.

To optimize for research, there are several ideas worth considering. Discussion is faster, taking only a single day, but requires at least 2 dwarves. Player testing has found discussion also awards more XP, (0-5 for pondering vs. 15-30 for discussion). So to optimize research, dwarves should be separated by topic/skill, with unskilled dwarves paired with skilled dwarves. This way, discussions will be equally divided between increasing the skilled dwarf's cycle count and the unskilled dwarf's cycle count. Only half the cycles will go to the skilled dwarf's cycle count, but discussion only takes a single day, so this is at net the same speed for the skilled dwarf with the additional bonus of the unskilled dwarf's cycle count also being increased. Both dwarves benefit from the increased XP gain.

Note that several topics benefit from skills that can be trained through faster means. Diagnostician and Wound Dresser can be trained through intentionally causing injuries or simply engaging in dangerous activities that require regular dwarf healthcare. Organizer can be trained through assigning make work to the manager, or Mechanic can be trained by spamming the creation of mechanisms. Skill level will increase much faster through these activities than through pondering or discussion. Thus, to optimize for producing breakthroughs in engineering topics, mechanics could first be quickly trained to a legendary within a year or two at only the cost of the stones for the mechanisms, and then assigned as a scholar.

Player testing has also found that visitors can come with research credits already done, thus, for forts aiming to maximize research, it makes sense to prioritize attracting wandering scholars.

Astronomy

These topics are relevant to astronomers.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Empirical observation	Methods of empirical observation in astronomy	Empirical evidence	Method	Astronomer
Path models	The method of forming precise models for the paths of astronomical objects	Orbit modeling	Method	Astronomer
Astrography	The creation of star charts	Star chart	n/a	Astronomer, Record keeper
Dates of lunar and solar eclipses	The dates of lunar and solar eclipses	Saros (astronomy)	n/a	Astronomer, Record keeper
Daylight variation with solar year	The variation of daylight with the seasons	Daytime § Daytime variations with latitude and seasons	n/a	Astronomer
Geocentrism	The theory that the sun moves around the world	Geocentric model	n/a	Astronomer
Height of tides vs moon and sun	The height of the tides, the moon and the sun	Pytheas § Pytheas on the tides and Tide	n/a	Astronomer
Heliocentrism	The theory that the world moves around the sun	Heliocentric model	n/a	Astronomer
Path of the moon	The path of the moon	Orbit of the Moon	n/a	Astronomer
Phases of the moon	The phases of the moon	Lunar phase	n/a	Astronomer
Precession of equinoxes	The precession of equinoxes over great periods of time	Axial precession	n/a	Astronomer, Record keeper
Relationship between lunar/solar year	The relationship between the lunar and solar year	Lunisolar calendar	n/a	Astronomer, Record keeper
Shape of the world	The shape of the world	Spherical Earth	n/a	Astronomer
Star catalogues 100	The compilation of information about stars	Star catalogue	n/a	Astronomer, Record keeper
Star catalogues 1000	The precise compilation of information about stars	Star catalogue	n/a	Astronomer, Record keeper
Star magnitude classification	The classification of stars according to brightness	Magnitude (astronomy)	n/a	Astronomer, Record keeper
Stellar Spectroscopy	The classification of stars according to color	Astronomical spectroscopy	n/a	Astronomer, Record keeper
Summer/winter moon	The rise of the moon according to the season	Lunar calendar	n/a	Astronomer
Summer/winter sun	The rise of the sun according to the season	Solar calendar	n/a	Astronomer
Tides and the moon	The relationship between the moon and the tides	Seleucus of Seleucia § Tides and Tide	n/a	Astronomer

Chemistry

These topics are relevant to chemists.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Adhesives	The preparation and use of adhesive materials	Adhesive	Chemicals	Chemist
Aqua regia	The preparation of aqua regia	Aqua regia	Chemicals	Chemist
Oil of vitriol	The preparation of oil of vitriol	Sulfuric acid	Chemicals	Chemist
Spirit of niter	The preparation of spirit of niter	Nitric acid	Chemicals	Chemist
Alkali and acids	The classification of alkali and acids	pH	Classification	Chemist, Record keeper
Combustibles	The classification of combustible materials	Combustibility	Classification	Chemist, Record keeper
Elemental theory	The classification of materials based on which elemental materials might form them	Classical element or Atomic theory	Classification	Chemist
Ores	The classification of ores	Ore	Classification	Chemist
Scratch test	A method of classifying the hardness of materials by scratching them against each other	Scratch hardness	Classification	Chemist, Record keeper
Alembic	The construction and use of the alembic	Alembic	Laboratory	Chemist
Blast furnace	The construction and use of the blast furnace	Blast furnace	Laboratory	Chemist
Crucible	The construction and use of the crucible	Crucible	Laboratory	Chemist
Lab ovens	The construction and use of laboratory ovens	Laboratory oven	Laboratory	Chemist
Systematic experiments	Methods for performing experiments systematically in the laboratory	Scientific method	Laboratory	Chemist, Record keeper
Theory of distillation	The theory and methods involved in distillation	Distillation	Laboratory	Chemist
Theory of evaporation	The theory and methods involved in evaporation	Evaporation	Laboratory	Chemist
Theory of liquid-liquid extraction	The theory and methods involved in the extraction of a constituent liquid from one solution to another	Liquid–liquid extraction	Laboratory	Chemist
Ampoule	The construction and use of the ampoule	Ampoule	Laboratory (glass)	Chemist
Beaker	The construction and use of the beaker	Beaker	Laboratory (glass)	Chemist
Flask	The construction and use of the flask	Flask	Laboratory (glass)	Chemist
Funnel	The construction and use of the funnel	Funnel	Laboratory (glass)	Chemist
Retort	The construction and use of the retort	Retort	Laboratory (glass)	Chemist
Vial	The construction and use of the vial	Vial	Laboratory (glass)	Chemist
Alloys	The mixing of metals to produce alloys	Alloy	Metallurgy	Chemist

Engineering

These topics are relevant to engineers.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Armillary sphere	The construction and use of armillary spheres	Armillary sphere	Astronomy	Mechanic
Astrolabe	The construction and use of the astrolabe	Astrolabe	Astronomy	Mechanic
Dioptra	The construction and use of the dioptra	Dioptra	Astronomy	Mechanic
Mural instrument	The construction and use of a mural instrument or mural quadrant	Mural instrument	Astronomy	Mechanic
Orrery	The construction and use of the orrery	Orrery	Astronomy	Mechanic
Spherical astrolabe	The construction and use of the spherical astrolabe	Astrolabe	Astronomy	Mechanic
Wood lamination	The use of lamination	Lamination	Construction	Mechanic
Models and templates	The use of models and templates in engineering	Prototype and Stencil	Design	Mechanic
Archimedes principle	The law of fluid displacement	Archimedes' principle	Fluid	Fluid engineer
Force pump	The construction and use of the force pump	Piston pump § Force pump	Fluid	Fluid engineer
Theory of siphon	The action of the siphon	Siphon	Fluid	Fluid engineer
Valves	The construction and use of valves	Valve	Fluid	Fluid engineer
Astrarium	The construction and use of the astrarium	Astrarium	Horology	Mechanic
Conical water clock	The use of conical shapes in water-based clocks to improve their accuracy	Water clock	Horology	Fluid engineer
Hourglass	The construction and use of the hourglass	Hourglass	Horology	Mechanic
Mechanical clock	The construction and use of mechanical clocks	Clock § Early mechanical clocks	Horology	Mechanic
Shadow clock	The use of shadows to tell direction and time	Sundial	Horology	Mechanic
Water clock	The use of water-based devices to tell time	Water clock	Horology	Fluid engineer
Water clock reservoir	The use of reservoirs in water-based clocks to improve their accuracy	Zhang Heng § Extra tank for inflow clepsydra	Horology	Fluid engineer
Balance wheel	The construction and use of the balance wheel.	Balance wheel	Machine	Mechanic
Bellows	The construction and use of the bellows	Bellows	Machine	Mechanic
Camshaft	The construction and use of the camshaft	Camshaft	Machine	Mechanic
Chain drive	The construction and use of chain drives	Chain drive	Machine	Mechanic
Chariot odometer	The construction and use of the chariot odometer	Odometer	Machine	Mechanic
Combination lock	The construction and use of the combination lock	Combination lock	Machine	Mechanic
Crank	The construction and use of the crank	Crank (mechanism)	Machine	Mechanic
Crankshaft	The construction and use of the crankshaft	Crankshaft	Machine	Mechanic
Differential gear	The construction and use of the differential gear	Differential (mechanical device)	Machine	Mechanic
Double acting piston bellows	The construction and use of the double-acting piston bellows	Bellows	Machine	Mechanic
Lever	The construction and use of the lever	Lever	Machine	Mechanic
Mechanical compass	The construction and use of the mechanical compass	Compass	Machine	Mechanic
Padlock	The construction and use of the padlock	Padlock	Machine	Mechanic
Piston	The construction and use of the piston.	Piston pump § Force pump	Machine	Mechanic
Pulley	The construction and use of the pulley	Pulley	Machine	Mechanic
Screw	The construction and use of the screw	Screw	Machine	Mechanic
Straight beam balance	The construction and use of the straight-beam balance	Weighing scale § Mechanical balances	Machine	Mechanic
Theory of gears	The reasons why gears are effective	Gear	Machine	Mechanic
Theory of lever	The reasons why the lever is effective	Lever	Machine	Mechanic
Theory of pulley	The reasons why pulleys are effective	Pulley	Machine	Mechanic
Theory of screw	The reasons why screws are effective	Screw	Machine	Mechanic
Theory of wedge	The reasons why the wedge is effective	Wedge	Machine	Mechanic
Theory of wheel and axle	The reasons why the wheel-and-axle construction is effective	Wheel and axle	Machine	Mechanic
Trip hammer	The construction and use of the trip-hammer.	Trip hammer	Machine	Mechanic
Tumbler lock	The construction and use of the tumbler lock	Pin tumbler lock	Machine	Mechanic
Verge escapement	The construction and use of the verge escapement	Verge escapement	Machine	Mechanic
Warded lock	The construction and use of the warded lock	Warded lock	Machine	Mechanic
Water-powered piston bellows	The construction and use of the water-powered piston bellows.	Du Shi § The Water-Powered Blast Furnace	Machine	Mechanic
Water-powered sawmill	The construction and use of the water-powered sawmill.	Watermill	Machine	Mechanic
Water-powered trip hammer	The construction and use of the water-powered trip hammer	Trip hammer and Water wheel	Machine	Mechanic
Water wheel	The construction and use of the water wheel.	Water wheel	Machine	Mechanic
Windlass	The construction and use of the windlass	Windlass	Machine	Mechanic
Atmospheric refraction	atmospheric refraction	Atmospheric refraction	Optics	Optics engineer
Camera obscura	The construction and use of the camera obscura	Camera obscura	Optics	Optics engineer
Cause of twilight	a precise explanation of the cause of twilight involving atmospheric refraction	Atmospheric optics	Optics	Optics engineer
Crystal lens	The construction and use of the crystal lens	Lens (optics) and Crystal	Optics	Optics engineer
Glass lens	The construction and use of the glass lens	Lens (optics) and Glass	Optics	Optics engineer
Height of atmosphere	The calculation of the height of the atmosphere based on atmospheric refraction	Atmosphere of Earth	Optics	Optics engineer
Law of refraction	The relation between refraction and the half chord	Snell's law	Optics	Mechanic
Parabolic mirror	The construction and use of the parabolic mirror.	Parabolic reflector	Optics	Optics engineer
Theory of color	The theory of light and color	Color theory	Optics	Optics engineer
Theory of rainbows	The appearance of rainbows based on optical theories	Rainbows	Optics	Optics engineer
Water-filled spheres	The construction and use of water-filled spheres as lenses	Lens (optics) and History of optics § Early history of optics	Optics	Optics engineer

Geography

These topics are relevant to geographers.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Accurate maps	The creation of accurate maps	Map	Cartography	Geographer
Cartography	The process involved in creating maps	Cartography	Cartography	Geographer
Distance scale	The use of distance scale in the creation of maps	Scale (map)	Cartography	Geographer
Economic	The placement of economic information on maps	Economic geography	Cartography	Geographer, Record keeper
Geological	The placement of geological information on maps	Geologic map	Cartography	Geographer
Grid system	The use of a grid system in the creation of maps	Grid reference	Cartography	Geographer
Height measurements	The measurement of the height of land features.	Topographic map and Levelling	Cartography	Geographer, Record keeper
Map projections	Methods of adjusting maps to account for the shape of the world	Map projection	Cartography	Geographer
Atlases	The collection of maps and other information together into a single text	Atlas	Form	Geographer, Record keeper
Econometrics	The process of economic data collection	Econometrics	Method	Geographer, Record keeper
Cartographical surveying	Surveying by triangulation for the purpose of creating maps	Cartography and Surveying	Surveying	Geographer
Engineering surveying	Surveying by triangulation for engineering projects	Construction surveying	Surveying	Geographer
Land surveying	Surveying by triangulation for the purpose of allocating land	Cadastral surveying	Surveying	Geographer
Military surveying	Surveying by triangulation for military purposes	Construction surveying and Military engineering	Surveying	Geographer
Surveying	The process of surveying land	Surveying	Surveying	Geographer
Surveying staff	The construction and use of the surveying staff	Level staff	Surveying	Geographer
Triangulation	Surveying by triangulation	Triangulation	Surveying	Geographer
Anemology	The forces that govern wind patterns	Global wind patterns	Theory	Geographer
Delta formation	The process of the formation of deltas at the mouths of rivers	River delta § Formation	Theory	Geographer
Latitude climate zones	The division of the world into climate zones	Clime	Theory	Geographer
Origin of rainfall from evap condense	The origin of rainfall through evaporation and condensation	Evaporation and Condensation	Theory	Geographer
Water cycle	A world-wide cycle involving precipitation, oceans, rivers, and other forms of water	Water cycle	Theory	Geographer

History

These topics are relevant to critical thinkers.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Alternate history	The exploration of how history would be different if some key past events had transpired differently	Alternate history	Form	Critical thinker
Autobiographical adventure	The method of writing a biography of oneself, particularly as it concerns a military campaign or adventure	Autobiography	Form	Critical thinker
Biographical dictionaries	The compilation of brief biographies into one large collection	Biographical dictionary	Form	Critical thinker
Biography	The method of writing the history of a single individual	Biography	Form	Critical thinker
Comparative anthropology	The method of comparing and contrasting different cultures	Cross-cultural studies	Form	Critical thinker
Comparative biography	The method of compiling several biographies to compare and contrast the subjects' character and to gain insight into history	Biography	Form	Critical thinker
Cultural history	The method of accurately and comprehensively describing cultures and civilizations	Cultural history	Form	Critical thinker
Encyclopedia	The compilation of many summaries into a single text.	Encyclopedia	Form	Critical thinker, Record keeper
Genealogy	The compilation of family lineages and methods of displaying them artfully	Genealogy	Form	Critical thinker, Record keeper
Treatise on tech evolution	The method of examining artifacts to determine how methods have changed over time.	Technological evolution	Form	Critical thinker
Archaeology	The method of collecting and evaluating artifacts to learn about history and culture	Archaeology	Sourcing	Critical thinker
Personal interviews	Using personal interviews as sources	Interview	Sourcing	Critical thinker, Organizer
Role of cultural differences	The role of cultural differences in source reliability and interpretation	Cultural relativism	Sourcing	Critical thinker
Role of state bias and propaganda	The role of state bias and propaganda in sources	Propaganda	Sourcing	Critical thinker
Role of systemic bias	The role of systemic bias in sources	Systemic bias	Sourcing	Critical thinker
Source reliability	The reliability of sources	Source criticism	Sourcing	Critical thinker
Historical causation	The causes of historical events	Causality § History	Theory	Critical thinker
Historical cycles	The notion of historical, governmental and social cycles	Cyclic history	Theory	Critical thinker
Social conflict	Conflict between members of a community	Social conflict	Theory	Critical thinker
Sociology	The notion of bonds between members of a community	Sociology	Theory	Critical thinker

Mathematics

These topics are relevant to mathematicians.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Divergence of harmonic series	The divergence of the harmonic series	Harmonic series (mathematics)	Algebra	Mathematician
Equations	The technique of balancing and completion for solving equations	The Compendious Book on Calculation by Completion and Balancing, Algebra, and Equation	Algebra	Mathematician
Large sums	Simple formulas for certain arbitrarily large sums	Summation	Algebra	Mathematician
Pascal's triangle	A triangular configuration of numbers relating to the successive powers of any sum	Pascal's triangle	Algebra	Mathematician
Quadratic by completing square	The solving of quadratic equations by completion of the square	Completing the square	Algebra	Mathematician
Quadratic formula	A formula which solves quadratic equations	Quadratic formula	Algebra	Mathematician
Solving higher order polynomials	Methods for solving certain equations involving powers higher than the quadratic	Galois theory	Algebra	Mathematician
Systems of equations	Methods of solving systems of equations	Linear system	Algebra	Mathematician
Area enclosed by line and parabola	The area enclosed by a parabola and a line	The Quadrature of the Parabola	Geometry	Mathematician
Area of circle		Area of a disk	Geometry	Mathematician
Area of triangle from side lengths	The computation of the area of a triangle from its three side lengths alone	Heron's formula	Geometry	Mathematician
Basic geometry	Geometric objects: points, lines, circles, triangles, and so on	Geometry	Geometry	Mathematician
Chords	The properties of chords	Chord (geometry)	Geometry	Mathematician
Chord tables	A table of chord lengths indexed by angle	Ptolemy's table of chords	Geometry	Mathematician
Conic sections	The categorization and properties of conic sections	Conic section	Geometry	Mathematician
Existence of pi	The relationship between the area of a circle and its radius, involving the ratio of the circumference of the circle to its diameter	Pi	Geometry	Mathematician
Geometric mean	The relationship between the length of the altitude of a right triangle and the lengths of the segments into which it divides the hypotenuse	Geometric mean theorem	Geometry	Mathematician
Inscribed triangle on diameter is right	The angles of triangles inscribed in a circle with one edge on the diameter	Thales' theorem	Geometry	Mathematician
Irrational numbers	The existence of incommensurable ratios	Irrational number	Geometry	Mathematician
Isosceles base angles equal	The equality of the base angle of isosceles triangles	Pons asinorum	Geometry	Mathematician
Law of sines	The relatonship between the half chords of lengths and the diameter of the triangle’s circumscribed circle.	Law of sines	Geometry	Mathematician
Pi to 6 digits		Zu Chongzhi § Mathematics and Milü	Geometry	Mathematician
Pythagorean theorem	The relationship between the lengths of the hypotenuse of a right triangle and the other two sides	Pythagorean theorem	Geometry	Mathematician
Pythagorean triples 3 digit	Examples of triples of large whole numbers which, when taken together, are the lengths of the sides of a right triangle	Pythagorean triples	Geometry	Mathematician
Pythagorean triples 4 digit	Examples of triples of very large whole numbers which, when taken together, are the lengths of the sides of a right triangle	Pythagorean triples	Geometry	Mathematician
Pythagorean triples small	Examples of triples of small whole numbers which, when taken together, are the lengths of the sides of a right triangle	Pythagorean triples	Geometry	Mathematician
Similar and congruent triangles	The properties of similar and congruent triangles	Similarity (geometry) and Congruence (geometry)	Geometry	Mathematician
Sum-difference trig identities	Trigonometric identities relating to the sums and differences of angles	List of trigonometric identities § Angle sum and difference identities	Geometry	Mathematician
Surface area of sphere	The computation of the surface area of a sphere	Sphere § Surface area	Geometry	Mathematician
Volume of cone	The computation of the volume of a cone	Cone § Volume	Geometry	Mathematician
Volume of pyramid	The computation of the volume of different pyramids	Pyramid (geometry) § Volume	Geometry	Mathematician
Volume of sphere	The computation of the volume of a sphere	Sphere § Volume	Geometry	Mathematician
Axioms	Axiomatic reasoning	Axiomatic system	Method	Logician
Method of exhaustion	An approximation of the ratio of a circumference of a circle to its diameter, using the area of polygons and the method of exhaustion	Method of exhaustion	Method	Logician
Proof by contradiction	The method of proof by contradiction	Proof by contradiction	Method	Logician
Algebra	Notation for abbreviating the unknown and other elements of an equation in a systematic and useful fashion	Algebra	Notation	Logician
Negative numbers	Notation for negative quantities	Negative number	Notation	Logician
Place values	Positional notation	Positional notation	Notation	Logician
Scientific notation	Notation for very large numbers	Scientific notation	Notation	Logician
Symbol for addition	The idea of using symbolic notation for addition	Plus and minus signs § Plus sign	Notation	Logician
Zero	A symbol for nothingness	0 (number)	Notation	Logician
Approximation of root 2	An approximation for the length of the diagonal of a square	Square root of 2 § History	Numbers	Mathematician
Chinese remainder algorithm	An algorithm for computing a number which has given remainders when divided by several given primes	Chinese remainder theorem	Numbers	Mathematician
Division	An algorithm for dividing one number into another, possibly yielding a remainder	Euclidean division	Numbers	Mathematician
Euclid's Theorem	A proof that there are infinitely many prime numbers	Euclid's theorem	Numbers	Mathematician
Euclidean Algorithm	An algorithm for computing the greatest common divisor of two numbers	Euclidean algorithm	Numbers	Mathematician
Irrationality of root 2	A proof that the length of a diagonal of a square is incommensurable with its edge	Square root of 2 § Proofs of irrationality	Numbers	Mathematician
Sieve algorithm for primes	An algorithm for calculating prime numbers	Sieve of Eratosthenes	Numbers	Mathematician
Unique prime factorization	The unique decomposition of a number into products of its prime divisors	Fundamental theorem of arithmetic	Numbers	Mathematician

Medicine

These topics are relevant to many medical professions, including doctors and diagnosticians.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Anesthesia	Anesthesia	Anesthesia	Method	Diagnostician
Asylum for mentally ill	The creation of asylums for the mentally ill.	Psychiatric hospital	Method	Critical thinker
Autopsy	The method of autopsy	Autopsy	Method	Diagnostician
Cataract surgery	Cataract surgery	Cataract surgery	Method	Surgeon
Cauterization	Cauterization	Cauterization	Method	Surgeon
Fracture immobilization	The method of fracture immobilization	Bone fracture § Immobilization	Method	Bone doctor
Fracture treatment	The treatment of fractures	Bone fracture § Treatment	Method	Bone doctor
Hernia surgery	Hernia surgery	Hernia § Surgery	Method	Surgeon
Hospital lab	The use of a laboratory for preparation of remedies in a hospital	Medical laboratory	Method	Critical thinker
Lithotomy surgery	The lithotomy surgery	Lithotomy	Method	Surgeon
Medical school	Schools of medicine	Medical school	Method	Critical thinker
Physical examination	The method of physical examination in diagnosing illness	Physical examination	Method	Diagnostician
Professional hospital staff	The use of professional hospital staff	Surgeon and Physician	Method	Critical thinker
Specialized wards	The use of specialized wards in hospitals	Hospital § Departments or wards	Method	Critical thinker
Tracheotomy surgery	The tracheotomy surgery	Tracheotomy	Method	Surgeon
Traumatic injuries	The treatment of traumatic injuries	Major trauma	Method	Diagnostician
Draining	The surgical method of draining	Drain (surgery)	Method (surgery)	Surgeon
Excision	The surgical method of excision	Surgery § Types of surgery	Method (surgery)	Surgeon
Incision	The surgical method of incision	Surgical incision	Method (surgery)	Surgeon
Ligature	The surgical method of ligature	Ligature (medicine)	Method (surgery)	Suturer
Probing	The surgical method of probing	Surgical instrument § Classification	Method (surgery)	Surgeon
Scraping	The surgical method of scraping	Surgical instrument § Classification	Method (surgery)	Surgeon
Suturing	The surgical method of suturing	Surgical suture	Method (surgery)	Suturer
Acute and chronic conditions	The distinction between acute and chronic conditions	Acute (medicine) and Chronic condition	Theory	Diagnostician
Anatomical studies	Anatomical studies for medical edification	Human body	Theory	Surgeon
Blood vessels	The distinction between veins and arteries	Blood vessel	Theory	Surgeon
Classification of bodily fluids	The classification of bodily fluids	Body fluid or Humorism	Theory	Surgeon
Classification of mental illnesses	The classification of mental illnesses	Mental disorder	Theory	Critical thinker, Diagnostician
Classification of muscles	The classification of muscles	Muscle	Theory	Surgeon
Comparative anatomy	Comparative anatomical studies for the use in medicine	Comparative anatomy	Theory	Surgeon
Convalescence	The theory of convalescence	Convalescence	Theory	Diagnostician
Disease and fouled water	The connection between disease and fouled water	Waterborne diseases	Theory	Critical thinker
Endemic disease	The theory of endemic disease	Endemic (epidemiology)	Theory	Diagnostician
Epidemic disease	The theory of epidemic disease	Epidemic	Theory	Diagnostician
Exacerbation	The notion of the exacerbation of a patient's condition	Exacerbation	Theory	Diagnostician
Eye anatomy	The anatomy of the eye	Human eye	Theory	Surgeon
Fracture classification	The classification of fractures	Bone fracture § Classification	Theory	Bone doctor
Motor vs sensory nerves	The distinction between motor and sensory nerves	Motor nerve and Sensory nerve	Theory	Surgeon
Nervous system function	The function of the nervous system	Nervous system	Theory	Diagnostician
Paroxysm	The notion of paroxysm	Paroxysmal attack	Theory	Diagnostician
Pathology	The classification of disease	Nosology	Theory	Diagnostician
Prognosis	Determining the likely outcome of a disease given a patient's current status	Prognosis	Theory	Diagnostician
Pulmonary circulation	Pulmonary circulation	Pulmonary circulation	Theory	Surgeon
Pulmonary medicine	Pulmonary medicine	Pulmonology	Theory	Diagnostician
Reaction time	The study of reaction time	Mental chronometry	Theory	Diagnostician
Relapse	The notion of relapse	Relapse	Theory	Diagnostician
Specialized surgical instruments	The use of specialized surgical instruments	Surgical instrument	Theory	Surgeon
Surgical models	The use of practice models in surgery	Anatomical model	Theory	Surgeon
The voice	The source of the voice	Phonation	Theory	Surgeon
Toxicology	The classification of toxic substances	Toxicology	Theory	Diagnostician
Treatment of mental illnesses	The treatment of mental illnesses	Treatment of mental disorders	Theory	Diagnostician
Animals as surgical models	The use of animals as surgical models	Vivisection	Tool	Surgeon
Animal remedies	Remedies prepared from animals	Traditional Chinese medicine § Animal substances	Tool	Diagnostician
Bandages	The method of bandaging wounds	Bandage	Tool	Wound dresser
Dedicated hospitals	The preparation and use of dedicated hospitals	Hospital	Tool	Critical thinker
Forceps	The construction and use of forceps	Forceps	Tool	Surgeon
Herbal remedies	Herbal remedies	Herbalism	Tool	Diagnostician
Mineral remedies	Mineral remedies	List of traditional Chinese medicines § Minerals	Tool	Diagnostician
Mud bags as surgical models	The use of mud bags as surgical models	Anatomical model	Tool	Surgeon
Needles	The construction and use of surgical needles	Surgical suture § Needles	Tool	Surgeon
Orthopedic cast	The creation and use of the orthopedic cast	Orthopedic cast	Tool	Bone doctor
Plants as surgical models	The use of plants as surgical models	Anatomical model	Tool	Surgeon
Scalpel	The construction and use of the scalpel	Scalpel	Tool	Surgeon
Surgical scissors	The construction and use of surgical sissors	Surgical scissors	Tool	Surgeon
Traction bench	The construction and use of the traction bench	Hippocratic bench	Tool	Bone doctor

Nature

These topics are relevant to naturalists and trackers.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Dissection	The dissection of creatures	Dissection	Method	Critical thinker
Anatomy	The anatomical study of creatures	Anatomy	Observation	Critical thinker, Tracker
Embryology	The embryological development of creatures	Embryology	Observation	Observer
Foraging behavior	The foraging behavior and diet of creatures	Foraging	Observation	Tracker, Record keeper, Observer
Migration	The migratory patterns of creatures	Animal migration	Observation	Tracker, Record keeper, Observer
Reproductive behavior	The reproductive behavior of creatures	Reproduction	Observation	Tracker, Record keeper, Observer
Social behavior	The social behavior of creatures	Social behavior	Observation	Tracker, Record keeper, Observer
Veterinary medicine	The diseases of creatures	Veterinary medicine	Observation	Tracker, Record keeper, Observer
Climactic adaptation	The way that creatures are suited to the climates in which they live	Climatic adaptation	Theory	Critical thinker
Comparative anatomy	The comparison of the anatomy of creatures	Comparative anatomy	Theory	Critical thinker
Food chain	The links between the diets of different creatures.	Food chain	Theory	Critical thinker
Physical taxonomy	The classification of creatures by their physical features	Aristotle's biology § Classification	Theory	Critical thinker
Struggle for existence	The struggle for survival among creatures	Struggle for existence	Theory	Critical thinker

Philosophy

These topics are relevant to logicians.

Topic	Description	Wikipedia link	Subdivision	Skills used in research
Nature of beauty	Discourse on the nature of beauty	Beauty (ancient thought)	Aesthetics	Critical thinker
Value of art	Discourse on the value of art	Aesthetics	Aesthetics	Critical thinker
Belief	Discourse on the nature of belief	Epistemology § Belief	Epistemology	Critical thinker
Justification	Discourse on the nature of justification	Epistemology § Justification	Epistemology	Critical thinker
Perception	Discourse on the nature of perception	Philosophy of perception	Epistemology	Critical thinker
Truth	Discourse on the nature of truth	Epistemology § Truth	Epistemology	Critical thinker
Individual value	Discourse on the meaning of individual happiness	Value (ethics) § Personal values	Ethics	Critical thinker
State consequentialism	Discourse on ethics as applied to the benefit of the state	State consequentialism	Ethics	Critical thinker
Interpersonal conduct	Discourse on ethics as applied to interpersonal conduct	Value (ethics) § Cultural values	Ethics (applied)	Critical thinker
Medical	Discourse on medical ethics	Medical ethics	Ethics (applied)	Critical thinker
Military	Discourse on ethics as applied to war	Ethics § Military ethics	Ethics (applied)	Critical thinker
Analogical inference	Analogical inference	Argument from analogy	Logic	Logician
Deductive reasoning	Deductive reasoning	Deductive reasoning	Logic	Logician
Dialectic reasoning	Dialectic reasoning. Books on this topic will instead talk about using the dialogue, as this opens up the dialogue literary form.	Dialectic	Logic	Logician
Direct inference	Direct inference	Statistical syllogism	Logic	Logician
Formal reasoning	Formal reasoning	Reason	Logic	Logician
Hypothetical syllogisms	Hypothetical syllogisms	Hypothetical syllogism	Logic	Logician
Inductive reasoning	Inductive reasoning	Inductive reasoning	Logic	Logician
Propositional logic		Propositional calculus	Logic
Syllogistic logic	Syllogistic logic	Syllogism	Logic	Logician
Causation	The nature of causation	Causality	Metaphysics	Critical thinker
Events	Discourse on the nature of events	Event (philosophy)	Metaphysics	Critical thinker
Existence	The nature of existence.	Existence	Metaphysics	Critical thinker
Mind body	Discourse on the nature of mind and body	Mind–body problem	Metaphysics	Critical thinker
Objects and properties	The relationship between objects and their properties	Essence	Metaphysics	Critical thinker
Processes	The nature of processes	Process philosophy	Metaphysics	Critical thinker
Time	Discourse on the nature of time	Time	Metaphysics	Critical thinker
Wholes and parts	The relationship between wholes and parts	Mereology	Metaphysics	Critical thinker
Education	Education, its forms and recommendations	Education	Specialized	Critical thinker
Law	Discourse on law	Law	Specialized	Critical thinker
Dictionary	Dictionaries	Dictionary	Specialized (language)	Critical thinker
Etymology	The notion of etymology	Etymology	Specialized (language)	Critical thinker
Grammar	Grammar	Grammar	Specialized (language)	Critical thinker
Diplomacy	Discourse on diplomacy	Diplomacy	Specialized (politics)	Critical thinker
Economic policy	Discourse on economic policy	Economic policy	Specialized (politics)	Critical thinker
Government forms	Discourse on government	Government	Specialized (politics)	Critical thinker
Social welfare	Discourse on social welfare	Welfare	Specialized (politics)	Critical thinker
Value agendas	The philosopher will choose a belief that they have and write about the "worthlessness/nuances/value of (belief)". Reading these books will result in a dwarf's (or adventurer's) values changing. [1] [2]	Propaganda	n/a

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If visitor scholars are allowed in a library, one should regularly check all books for nature-related value agenda to prevent fortress citizens from wandering off to start a dwarven forest retreat.